1. Field of the Invention
The invention generally relates to analog filter circuits, and more particularly to a method and apparatus for fine tuning and adjusting the cut-off frequency and voltage gain of an active filter.
2. Description of the Prior Art
A filter is an important and familiar component in signal processing systems; and the purpose of the filter is to eliminate the band signals unwanted for retaining and amplifying the band signals desired. Integrating the filters into one chip is a common trend in the manufacture process of the advanced integrated circuit, especially to the communication markets. As the communication system continuously develops, the signal-processing circuits not only require high performances, but also should have a multi-function for a system to process different types of signals. For instance, the 2nd/3rd generation cell phone in wireless communication and V/ADSL (i.e. very high data/asymmetrical digital subscriber line) modem in wired communication all require the filters that can be switched in both systems. Therefore, how to design a filter, which can program the cut-off frequency to an accurate value within a large range, is a main key point in today's signal processes of the communication systems.
The cut-off frequency of a filter is in direct proportion to the reciprocal of time constant τ (i.e. f=½πτ), and the time constant τ is the product of equivalent resistance and capacitance (i.e. τ=R×C) of the active RC filter. In general, the programmable active RC filters finely tune the value of the cut-off frequency by adjusting the number of operative cells of the resistance or the capacitance. FIG. 1A depicts a conventional programmable filter with a selective parallel-capacitor circuit structure, the situations (off and on) of the switch devices b0, b1, b2, b3 can determine whether the capacitors connected with the filter are operative or not. Since each of the capacitors is connected in parallel, so that the equivalent capacitance of the filter circuit can be obtained by adding the capacitance of the capacitors connected with the switch devices b0, b1, b2, b3 that is operative. For instance, the equivalent capacitance of the circuit is 0 when the switch devices b0, b1, b2, b3 are all turned off; similarly, the equivalent capacitance of the circuit is 15C when the switch devices b0, b1, b2, b3 are all turned on. Thus, the combination of the switch devices b0, b1, b2, b3 is the control code of the circuit that can be used to control the equivalent capacitance of the filter and then can achieve the purpose of fine tuning the cut-off frequency. In addition, it can also obtain the same purpose by using the selective parallel-resistor circuit (referring to FIG. 1B) or the selective series-resistor circuit (referring to FIG. 1C) structure to substitute for resistor R1 in FIG. 1A.
According to the fundamental principle of active filters, the cut-off frequency is in direct proportion to the reciprocal of the product of equivalent resistance and equivalent capacitance of the circuit (i.e. f=½πτ=1/(2πR×C)). Hence, the relation between the control code and the cut-off frequency of the filter is non-linear regardless of equivalent resistance or equivalent capacitance is tuned, which is shown in FIG. 2A. In applications, besides, when the cut-off frequency is required that being adjusted within certain accuracy, the number of control bits will be determined by the largest slope parts in FIG. 2A. It is therefore that, it will increase the number of devices of the circuits and reduce the control efficiency; thus, it will make it become difficult to design in an integrated circuit. In addition, since the cut-off frequency of such kind of filters can only be tuned within a fixed range, the applications of that are limited in the kind of filters.
Accordingly, it can become a linear relation (as is shown in FIG. 2B) between the control code and the cut-off frequency by making the relations between the control code and the reciprocal of equivalent resistance (i.e. the equivalent conductance) of the filter more linear. Therefore, it can not only increase the control efficiency and reduce the area of the circuits, but also extend the tuning range of cut-off frequency and add the applications of the circuits for the multi-function purpose.